Multi-Robot Motion Planning via Parabolic Relaxation

Choi, Changrak; Adil, Muhammad; Rahmani, Amir; Madani, Ramtin

doi:10.1109/lra.2022.3171075

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…By avoiding central synchronization, their approach offers significant speedups, but at the potential cost of suboptimal paths. Choi et al [41] explored parabolic relaxation techniques for motion planning, providing a unique intersection between computational geometry and optimization. However, the method may struggle with environments having numerous narrow passages due to its relaxed nature.…”

Section: Number Of Robots and W-number Of Squaresmentioning

confidence: 99%

On the Intersection of Computational Geometry Algorithms with Mobile Robot Path Planning

Latif,

Parasuraman

2023

Algorithms

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In the mathematical discipline of computational geometry (CG), practical algorithms for resolving geometric input and output issues are designed, analyzed, and put into practice. It is sometimes used to refer to pattern recognition and to define the solid modeling methods for manipulating curves and surfaces. CG is a rich field encompassing theories to solve complex optimization problems, such as path planning for mobile robot systems and extension to distributed multi-robot systems. This brief review discusses the fundamentals of CG and its application in solving well-known automated path-planning problems in single- and multi-robot systems. We also discuss three winning algorithms from the CG-SHOP (Computational Geometry: Solving Hard Optimization Problems) 2021 competition to evidence the practicality of CG in multi-robotic systems. We also mention some open problems at the intersection of CG and robotics. This review provides insights into the potential use of CG in robotics and future research directions at their intersection.

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Section: Number Of Robots and W-number Of Squaresmentioning

confidence: 99%

On the Intersection of Computational Geometry Algorithms with Mobile Robot Path Planning

Latif,

Parasuraman

2023

Algorithms

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“…are given matrices/scalars. The formulation (11a) -(11c) is motivated by a wide-variety of applications including problems involving tensor products [21,86]. A case study of optimization for dynamical systems is provided in the second part.…”

Section: Parabolic Relaxation For Tensor Qcqpmentioning

confidence: 99%

Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties

Madani¹,

Ashraphijuo²,

Kheirandishfard³

et al. 2022

Preprint

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For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible set is contained on the boundary of the parabolic relaxation. Under certain assumptions, this property enables one to recover near-optimal feasible points via objective penalization. Moreover, through an appropriate change of coordinates that requires a one-time computation of an optimal basis, the easier-to-solve parabolic relaxation can be made as strong as a semidefinite programming (SDP) relaxation, which can be effective in accelerating algorithms that require solving a sequence of convex surrogates. The majority of theoretical and computational results are given in the next part of this work [57].

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